Exhibit 4.11

AGREEMENT

This AGREEMENT(this
Agreement) is made effective as of April 19, 2011 among PARAGON SHIPPING INC., a Marshall Islands company (Paragon Shipping), BOX SHIPS INC., a Marshall Islands company (Box Ships) and Michael
Bodouroglou, a natural person (Bodouroglou).

WHEREAS, Paragon Shipping is engaged in the ownership,
operation and chartering of drybulk carrier vessels and is a shareholder of more than five per cent of the issued and outstanding common shares of Box Ships, and certain of the senior executive officers of Paragon Shipping also serve as senior
executive officers of Box Ships;

WHEREAS, Box Ships is or will be engaged in the ownership, operation and chartering of container
vessels;

WHEREAS, Paragon Shipping has granted to Box Ships the right to acquire one or both of two container vessels
that Paragon Shipping has contracted to build (the Option Vessels) pursuant to a purchase option agreement between Paragon Shipping and Box Ships dated as of the date hereof (the Purchase Option Agreement).

WHEREAS, Paragon Shipping and Box Ships desire to enter into this agreement to memorialize their agreement relating to
engaging in competing business activities and certain other matters set forth more fully herein.

NOW, THEREFORE, in
consideration of the mutual covenants and premises of the parties hereto and for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the parties agree as follows:



| | 1. | Non-Competition Agreement
| | -- | -------------------------

(a)        For so long as (i) Bodouroglou is a member of the board of directors or an executive officer of Paragon Shipping and of Box Ships and
(ii) Paragon Shipping is the beneficial owner of not less than 5% of the total issued and outstanding common shares of Box Ships, Paragon Shipping shall not, directly or indirectly, acquire, charter, enter into any proposal or agreement to
acquire or charter or enter into contract for the construction of, any containership vessel or any business related to the ownership or operation of container vessels without the prior written consent of Box Ships.

(b)        For so long as (i) Bodouroglou is a member of the board of
directors or an executive officer of Box Ships and of Paragon Shipping and (ii) Paragon Shipping is the beneficial owner of not less than 5% of the total issued and outstanding common shares of Box Ships, Box Ships shall not, directly or
indirectly, acquire, charter, enter into any proposal or agreement to acquire or charter or enter into contract for the construction of, any drybulk carrier or any business related to the ownership or operation of drybulk carrier without the prior
written of Paragon Shipping.

(c)        For so long as Bodouroglou is
a member of the board of directors of Box Ships, neither Bodouroglou nor any entity controlled by Bodouroglou shall, directly or indirectly, acquire, charter, enter into any proposal or agreement to acquire or charter or enter into contract for the
construction of, any containership vessel or any business



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related to the ownership or operation of container vessels without the prior written consent of Box Ships.

(d)        Not withstanding any other provision of this Agreement, nothing herein
shall be deemed to prevent or limit any entity owned or controlled by Bodouroglou, including with limitation Allseas Marine S.A., from providing vessel management services to any class, sector or type of vessel.

2.        Box Ships Purchase Option and Waiver. Notwithstanding any other provision of
this Agreement, Box Ships hereby acknowledges and agrees that in the event that Box Ships does not exercise its option to purchase one or both of the Option Vessels pursuant to the Purchase Option Agreement, the (i) Paragon Shippings
ownership, operation or sale of such Option Vessels or Option Vessel shall not violate any provision of this Agreement and (ii) Paragon Shipping shall be entitled to charter the vessel on a period charter commencing not more than 45 days after
the delivery of the vessel to Paragon Shipping (the Initial Option Vessel Charter).



| | 3. | Right of First Refusal over Charters.
| | -- | -------------------------------------

(a)        For so long as (i) Bodouroglou is a member of the board of directors or an executive officer of Paragon Shipping and of Box Ships and
(ii) Paragon Shipping is the beneficial owner of not less than 5% of the total issued and outstanding common shares of Box Ships, Paragon Shipping shall grant to Box Ships a right of first refusal over any employment opportunity for a container
vessel presented or available to Paragon Shipping with respect to any vessel owned, directly or indirectly, by it (the Charter Opportunity) in accordance with Section 3(b), below, provided however, that this Section 3
shall not be applicable to an Initial Option Vessel Charter with respect to one or both of the Option Vessels.

(b)        In the event Paragon Shipping receives an offer for or negotiates a
Charter Opportunity relating to a container vessel for which a container vessel of Box Ships which meets the charterers requirements relating to, among other factors, suitability, specifications, positioning, size, and cost is available for
charter at such time, then prior to entering into such Charter Opportunity, Paragon Shipping shall notify Box Ships of such Charter Opportunity. Within seven (7) days after receipt of such notice from Paragon Shipping, Box Ships shall have the
right to exercise its right of refusal and enter into the Charter Opportunity. In the event that Box Ships does not exercise its right of first refusal on or before the seventh day following receipt of the notice from Paragon Shipping, Paragon
Shipping shall be entitled to pursue such Charter Opportunity.



| | 4. | Right of First Offer on Sale of Vessels.
| | -- | ----------------------------------------

(a)         For so long as (i) Bodouroglou is a member of the board of directors or an executive officer of Paragon Shipping and of Box Ships and
(ii) Paragon Shipping is the beneficial owner of not less than 5% of the total issued and outstanding common shares of Box Ships, Paragon Shipping agrees to grant a right of first offer to Box Ships on any sale of any container vessel owned by
Paragon Shipping prior to the sale of such vessel to any other party.



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(b)        In the event that Paragon
Shipping proposes to sell any container vessel that it owns during the term of the right of first offer, Paragon Shipping shall notify Box Ships of such intention to sell the vessel (an Option Notice). At any time not later than
thirty (30) days following the receipt of an Option Notice, Box Ships shall have the right to make a written offer (the Purchase Offer) to Paragon Shipping setting forth the materials terms of a proposed purchase of the
vessel. Paragon Shipping shall have fifteen (15) days to either accept or reject such Purchase Offer by written notice to Box Ships. In the event that a Purchase Offer is accepted, the parties shall proceed with the purchase and sale of the
vessel as soon as practicably after entry into customary documentation for such transaction. In the event that the Purchase Offer is not accepted by Paragon Shipping, Paragon Shipping may sell the vessel to a third party at any time within ninety
(90) days of the receipt of the Purchase Offer for a price of not less than the price set forth in the Purchase Offer. If such vessel is not sold within ninety days of the receipt of the Purchase Offer or is proposed to be sold on terms more
favorable to a buyer than contained in the Purchase Offer, such vessel must be offering to Box Ships in accordance with the terms of this Section 4 of this Agreement.

3.        Confidentiality. Except as (i) the parties may otherwise agree or (ii) as may be required by either party in the disclosing partys
reasonable opinion after consultation with outside legal counsel by applicable law (including without limitation U.S. federal securities law) or compliance with the requirements of any regulatory authority or stock exchange on which the shares of a
party may be listed, any non-public information or confidential information relating to or obtained pursuant to this Agreement or any transaction contemplated hereby, or the business or affairs of either party, their respective subsidiaries or
affiliates, shall be kept strictly confidential by the other party hereto; provided, however, in the case of clause (ii) of this Section 4, prior to any public disclosure by a party hereto contemplated to be made in order to comply with
applicable law or requirements of regulatory authorities or stock exchange requirements, the disclosing party shall provide a draft of such public disclosure or other communication to the non-disclosing party in advance and consult with the
non-disclosing party regarding the contents of such disclosure and, to the extent reasonably practicable under the circumstances, take into consideration any comments on such disclosure as may be provided by the non-disclosing party.

4.        Notices. Each notice, consent or request required to be given to a party hereto
pursuant to this Agreement must be given in writing. A notice may be given by delivery to an individual or by fax, and shall be validly given if delivered on a business day to an individual at the following address, or, if transmitted on a Business
Day, by fax or email addressed to the following Party:



|                                                                                                             |  |                                                                                                    |  | 
|------------------------------------------------------------------------------------------------------------ |  | -------------------------------------------------------------------------------------------------- |  | 
|If to Paragon Shipping Inc.: 
15 Karamanli Avenue 16673 Voula,
Greece +30 210 89 95 088
info@paragonship.com |  | If to Box Ships Inc.: 
15 Karamanli Avenue 16673 Voula,
Greece +30 210 89 95 088
info@boxships.com |  | 



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5.        Governing Law. This Agreement and
the rights and obligations of the parties hereto will be governed by and construed in accordance with the laws of the State of New York.

6.        Further Assurances. Each of the parties to this Agreement agrees to execute, acknowledge and deliver all such instruments and take all such actions
a party from time to time may reasonably request in order to further effectuate the purposes of this Agreement and to carry out the terms hereof.

7.        Binding Effect; Assignment. This Agreement will be binding upon and inure to the benefit of the parties hereto and to their respective heirs,
executors, administrators, successors and permitted assigns. This Agreement is not assignable by any party without the prior written consent of each of the other parties.

8.        Severability. If any term, covenant or condition of this Agreement is held to be invalid, illegal or unenforceable in any respect, then this
Agreement will be construed as if such invalid, illegal, or unenforceable provision or part of a provision had never been contained in this Agreement.

9.        Counterparts. This Agreement may be executed in multiple counterparts, each of which will be deemed an original and all of such counterparts
together will constitute one agreement. To facilitate execution of this Agreement, the parties may execute and exchange counterparts of signature pages by telephone facsimile.

[Signature page follows.]



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IN WITNESS WHEREOF, this Agreement has been duly executed by the parties as of the
date first written above.



|                                                         |  | 
|-------------------------------------------------------- |  | 
|PARAGON SHIPPING INC.                                   
|                                                         | 
|/s/ George Skrimizeas                                    |  | 
|Name: George Skrimizeas Title:   Chief Operating Officer
|                                                        
|BOX SHIPS INC.                                          
|                                                         | 
|/s/ Robert Perri                                         |  | 
|Name: Robert Perri Title:   Chief Financial Officer     
|                                                        
|MICHAEL BODOUROGLOU                                     
|                                                         | 
|/s/ Michael Bodouroglou                                  |  | 
|                                                         |  | 

[Signature Page to Non-Compete Agreement]



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